Econ 441
Fall Term 2008
Alan Deardorff
Midterm Exam No. 1 Answers
Page 1 of 6
Midterm Exam No. 1 - Answers
October 6, 2008
Answer all questions on these sheets. Plan and budget your time. The questions are
worth a total of 60 points, as indicated, and you will have 80 minutes to complete the
exam.
1. (6 points) There are two ways to justify the use of community indifference curves to
represent the quantities of goods that an economy of many consumers will demand.
One way uses a single assumption, which you should indicate in column 1 below.
The other uses two assumptions together, both of which you should indicate in
column 2 below. Thus, you should insert one check mark () in the column labeled 1
and two check marks in the column labeled 2, in order to indicate the two ways of
justifying community indifference curves.
1
2
a. Consumers require a positive quantity of each good,
regardless of prices.

b. Preferences are homothetic
c. Consumers wish to consume more of the capital-intensive
good than the labor-intensive good.
d. The value of consumption equals income

e. The distribution of income is fixed.
f. Consumers are willing to substitute one good for another
when prices change.

g. Preferences of all consumers are the same.
2. (4 points) The table shows output per unit labor for two countries and two goods. If
these are the only countries and only goods in the world, indicate the country that…
Output produced per
unit of labor
…has comparative advantage in good X:
…has absolute advantage in good Y:
B
B
Country
Good
X
Y
A
50
500
B
100
600
Econ 441
Fall Term 2008
Alan Deardorff
Midterm Exam No. 1 Answers
Page 2 of 6
3. (6 points) The figure below shows a production Edgeworth Box, with origins
indicated for the inputs of capital, K, and labor, L, into production of goods X and Y.
Eight isoquants are shown, reflecting standard constant-returns-to-scale production
functions. These are labeled Q0 ,…, Q7 at the left ends of the isoquants, but it is left to
you to know which good, X or Y, these refer to and which of these quantities are
larger or smaller than others.
figure,
 draw the efficiency locus that is implied by these
a. (2 points) In the
isoquants.
b. (4 points) On the axes below, draw the production possibility frontier for this
economy, and identify along the appropriate axes the eight quantities Q0 ,…, Q7 .


Econ 441
Fall Term 2008
Alan Deardorff
Midterm Exam No. 1 Answers
Page 3 of 6
4. (10 points) Consider an economy that produces and consumes two goods, X and Y, in
autarky and free trade. In autarky it produces quantities X pa , Ypa and consumes
quantities X ca , Yca , at prices pXa , pYa . In free trade it faces world prices pWX , pYW , and at
those prices it produces X pf , Ypf and consumes X cf , Ycf . Using this notation in the
space below, state and prove – using appropriate
 equations and inequalities – that this
economy
gains (orat least does not lose) from trade. Be sureto state the assumptions

that you use, and indicate where in the proof these assumptions are used.


Assumption 1: Competitive industries maximize the value of national output at the
prevailing prices.
Assumption 2: Trade is balanced (thus expenditure equals income)
Theorem (Gains from Trade): Economic welfare of a country is at least as great with
free trade as in autarky. Or, more formally, at free trade prices consumers could
afford to buy what they bought in autarky:
pWX X cf  pYW Ycf  pWX X ca  pYW Yca
Proof:


pWX X cf  pYW Ycf  pWX X pf  pYW Ypf
by Assumption 2
 pWX X pa  pYW Ypa
by Assumption 1
 pWX X ca  pYW Yca
by definition of autarky
Econ 441
Fall Term 2008
Alan Deardorff
Midterm Exam No. 1 Answers
Page 4 of 6
5. (5 points) The figure below shows the production possibility frontier for a Ricardian
economy able to produce two goods, X and Y. The table at the right lists five sets of
prices for X and Y. In the columns headed X and Y, record the quantity that this
economy will produce of each good at those prices.

pX
pY
X
Y
$8
$2
5
0
 $8
$12
 0
10
0
10
$1.20 $1.20
$1
$0.49
5
0
€3
€9
0
10
6. (17 points) The solid straight lines in the figures below are the production possibility
frontiers (PPFs) of the (only) two countries in a Ricardian model. The curves are
members of their families of community indifference curves. The dashed straight line
is an iso-value line for the prices that clear world markets with free trade. Using the
scales on the axes and your knowledge of how the Ricardian model works, identify
and record in the table on the next page the quantities and prices requested.
Econ 441
Fall Term 2008
Alan Deardorff
Midterm Exam No. 1 Answers
Page 5 of 6
In autarky:
In Country A:
The relative price of X: pX pY
2
Production of X
2
Y
Consumption of
6
In Country B:
Production of Y
6
In free trade:
The (world) relative price of X: pX pY
1
In Country A:
Production of X 
0
Consumption of X
4
Exports (+) or imports (–) of X
–4
Production of Y
10
Consumption of Y
6
Exports (+) or imports (–) of Y
+4
In Country B:
Production of X
8
Consumption of X
4
Exports (+) or imports (–) of X
+4
Production of Y
2
Consumption of Y
6
Exports (+) or imports (–) of Y
–4
Econ 441
Fall Term 2008
Alan Deardorff
Midterm Exam No. 1 Answers
Page 6 of 6
7. (12 points) In the space below, draw a diagram representing a free-trade equilibrium
for a small-open, two-good Ricardian economy that is completely specialized in
production of good X.
a. (4 points) In your diagram, show the effect on this economy of an increase in the
world relative price of good X. Assume that preferences are homothetic.
b. (7 points) Guided by your answer to part (a), but also considering how you might
have drawn it differently for valid production possibilities, preferences, and
prices, indicate what happens to the variables listed below. That is, for each
variable indicate in the blanks provided whether the stated variable necessarily
rises (+), necessarily falls (–), necessarily stays the same (0), or could either rise
or fall depending on how you draw the curves (?). Thus you will enter one of the
four symbols, +, –, 0, or ?, in each blank.
i.
Production of X
0
ii.
Production of Y
0
iii.
Consumption of X
?
iv.
Consumption of Y
+
v.
Quantity of exports
?
vi.
Quantity of imports
+
vii.
Welfare (i.e., utility, as given by indifference curves)
+or ?